Stat 401, Section F Homework 2
Due Date: Wednesday, September 5
Please do not include any computer output besides graphs. All other information should be copied
from R into your written answer.
1. Each of the following situations requires a significance test about a population mean µ. State the appro-
priate null hypothesis H0:µ=? and alternative hypothesis Hain each case.
(a) The mean area of the several thousand apartments in a new development is advertised to be 1250
square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an
engineer to measure a sample of apartments to test their suspicion.
(b) Larry’s car averages 32 miles per gallon on the highway. He now switches to a new motor oil that is
advertised as increasing gas mileage. After driving 3000 highway miles with the new oil, he wants
to determine if his gas mileage actually has increased.
(c) The diameter of a spindle in a small motor is supposed to be 5 millimeters. If the spindle is either
too small or too large, the motor will not perform properly. The manufacturer measures the diameter
in a sample of motors to determine whether the mean diameter has moved away from the target.
2. A cheese company suspects that a milk supplier is watering down milk to increase profits. The freezing
point of natural milk follows a normal distribution with mean µ=−0.545 degrees Celsius. Added water
raises the freezing temperature toward 0degrees C. The freezing temperature of 15 lots of the suppliers
milk is measured. The average of the 15 measurements is ¯
Y=−0.538 degrees C. The standard deviation
of the 15 measurements is s= 0.008. Is this good evidence that the supplier is adding water to the milk?
(a) Write down the null and alternative hypotheses.
(b) Compute a test statistic (t−ratio).
(c) Determine the p-value.
(d) Provide a conclusion.
3. The authors of a scientific article wrote, “Sixteen rats weighing 150 ±10 g were injected . . .”. 150 g
seems to be the average weight of the 16 rats in the sample. The 10 g figure is a little ambiguous and
could be interpreted in several different ways.
(a) If the authors wished to directly convey information about the variation among the weights of the
sixteen rats in the sample, should 10 g represent the sample standard deviation or the standard error
of the sample mean/average?
(b) Suppose 10 g really represented the standard error of the sample mean. What must have been the
sample standard deviation of the 16 rats?
(c) Suppose 150±10 g really represented a 95% confidence interval for the mean weight of a population
of rats. What must have been the sample standard deviation of the 16 rats?
4. A plant physiologist grew 13 individually potted soybean seedlings of the type called Wells II. She raised
the plants in a greenhouse under identical environmental conditions. She measured the total stem length
(in cm) for each plant after 16 days of growth. The data are provided below.
20.2 22.0 19.7 22.9 22.1 21.5 23.3 22.0 20.9 20.0 21.9 19.4 21.5
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